Revising the ensemble-based Kalman filter covariance for the retrieval of deep-layer soil moisture

Previous studies have demonstrated that soil moisture in the top layers (e.g., within the top 1-m depth) can be retrieved by assimilating near-surface soil moisture observations into a land surface model using ensemble-based data assimilation algorithms. However, it remains a challenging issue to provide good estimates of soil moisture in the deep layers, because the error correlation between the surface and deep layers is low and hence is easily influenced by the physically limited range of soil moisture, probably resulting in a large noise-to-signal ratio. Furthermore, the temporally correlated errors between the surface and deep layers and the nonlinearity of the system make the retrieval even more difficult. To tackle these problems, a revised ensemble-based Kalman filter covariance method is proposed by constraining error covariance estimates in deep layers in two ways: 1) explicitly using the error covariance at the previous time step and 2) limiting the increase of the soil moisture error correlation with the increase of the vertical distance between the two layers. This method is then tested at three separate point locations representing different precipitation regimes. It is found that the proposed method can effectively control the abrupt changes of error covariance estimates between the surface layer and two deep layers. It significantly improves the estimates of soil moisture in the two deep layers with daily updating. For example, relative to the initial background error, after 150 daily updates, the error in the deepest layer reduces to 11.4%, 32.3%, and 27.1% at the wet, dry, and medium wetness locations, only reducing to 62.3%, 80.8%, and 47.5% with the original method, respectively. However, the improvement of deep-layer soil moisture retrieval is very slight when the updating frequency is reduced to once every three days.